Well if you can find a way to do EQ on your Mac, then that's the best solution, you'll want a solution that is able to implement parametric filters.
K712 does look like it has more bass, but the frequency response looks messed up to me:
https://www.dropbox.com/s/l0ucv96zjjp8cvv/AKG K712.pdf?dl=0
K702 is similar to the K702 Anniversary Edition listed at the following link and is a more accurate frequency response:
https://www.dropbox.com/s/j6yr8g87j2nb1yo/AKG K702 65th Anniversary Edition.pdf?dl=0
Those are links to Oratory's EQ's who's generally the most respected headphone EQ resource.
If you're not gonna EQ though, then I recommend the Sennheiser HD600 as it's a really quite accurate frequency response, and in my experience they're the best sounding headphone I've ever heard without EQ:
https://www.dropbox.com/s/dm0m6u3s3b4zqzl/Sennheiser HD600.pdf?dl=0
But if you're gonna EQ then I recommend the K702 and following my EQ I posted you - but it's possible you won't like it, you kind of have to know if you like the Headphone Harman Curve. K702 also has reliability issues which I described, but if you're happy fixing them as I do then why not. I love this headphone for it's fantastic imaging & soundstage and to me they sound more like speakers than any headphone I've ever tried.
If I was you, I'd try to find out if you like the Headphone Harman Curve, so have you got a headphone at the moment that is on any of the following 2 lists, if you do then learn how to apply the EQ and listen to them and see if you think the EQ improves the sound. If it sounds good then get Sennheiser HD600 if you don't want to EQ them on a daily basis for whatever reason, but if you're gonna do most of your listening EQ'd then I'd say go with K702 if you can live with the reliability issues. So check if your current headphones are at either two of these lists:
https://www.reddit.com/r/oratory1990/wiki/index/list_of_presets
https://github.com/jaakkopasanen/AutoEq/blob/master/results/RANKING.md
Headphones are such personal things in terms of what is preferred, as the headphone interacts differently with different people's physical anatomy (the topic of HRTF), so preference for a certain headphone is so much more unpredictable than recommending a speaker to someone....but if you do what I suggest in my previous paragraph that will give you an idea if the Headphone Harman Curve sounds good to you, and that's the best starting point in trying to find a headphone that sounds right & good to you.
EDIT: You asked me about earcup size. K702 is circular inside and about 6cm in diameter. HD600 (& I guess HD650) is about 7cm long by 4cm wide, so with your ears struggling to fit inside HD650 you have to ask yourself if that was because your ears were to long or too wide. HD650 is pretty roomy though as far as headphones go, so you must have pretty big ears indeed, so that is a good question for you to ask. Yep, K702 is 6cm in internal diameter (circular inside, not oval).